DLMF:18.9.E6 (Q5602)

From DRMF
Revision as of 15:22, 2 January 2020 by Admin (talk | contribs) (‎Changed an Item: Add constraint)
(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)
Jump to navigation Jump to search
No description defined
Language Label Description Also known as
English
DLMF:18.9.E6
No description defined

    Statements

    Defining formula
    ( n + 1 2 ⁢ α + 1 2 ⁢ β + 1 ) ⁢ ( 1 + x ) ⁢ P n ( α , β + 1 ) ⁡ ( x ) = ( n + 1 ) ⁢ P n + 1 ( α , β ) ⁡ ( x ) + ( n + β + 1 ) ⁢ P n ( α , β ) ⁡ ( x ) , 𝑛 1 2 𝛼 1 2 𝛽 1 1 𝑥 Jacobi-polynomial-P 𝛼 𝛽 1 𝑛 𝑥 𝑛 1 Jacobi-polynomial-P 𝛼 𝛽 𝑛 1 𝑥 𝑛 𝛽 1 Jacobi-polynomial-P 𝛼 𝛽 𝑛 𝑥 {\displaystyle{\displaystyle(n+\tfrac{1}{2}\alpha+\tfrac{1}{2}\beta+1)(1+x)P^{% (\alpha,\beta+1)}_{n}\left(x\right)=(n+1)P^{(\alpha,\beta)}_{n+1}\left(x\right% )+(n+\beta+1)P^{(\alpha,\beta)}_{n}\left(x\right),}}
    0 references
    DLMF id
    DLMF:18.9.E6
    0 references
    Symbols used
    Q11660
    Defining formula
    P n ( α , β ) ⁡ ( x ) Jacobi-polynomial-P 𝛼 𝛽 𝑛 𝑥 {\displaystyle{\displaystyle P^{(\NVar{\alpha},\NVar{\beta})}_{\NVar{n}}\left(% \NVar{x}\right)}}
    xml-id
    C18.S3.T1.t1.r2.m2acdec
    0 references
    Q11726
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C18.S1.XMD6.m1fdec
    0 references
    Q11727
    Defining formula
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C18.S2.XMD3.m1edec
    0 references
     
        Retrieved from "https://drmf-beta.wmflabs.org/index.php?title=Item:Q5602&oldid=57219"